Terminal Velocity

When an object which is falling under the influence of gravity or subject to some other constant driving force is subject to a resistance or drag force which increases with velocity, it will ultimately reach a maximum velocity where the drag force equals the driving force. This final, constant velocity of motion is called a "terminal velocity", a terminology made popular by skydivers. For objects moving through a fluid at low speeds so that turbulence is not a major factor, the terminal velocity is determined by viscous drag. The expression for the terminal velocity is of the form

Quadratic Velocity Dependence

For large objects moving through air, the air resistance is approximately proportional to the square of the velocity. The form of the resistance is

where ρ is the air density, A the crosssectional area, and C is a numerical drag coefficient. The drag coefficient C is 0.5 for a spherical object and can reach 2 for irregularly shaped objects according to Serway. An object falling through the air will reach a terminal velocity when the drag force is equal to the weight:

Hailstone Terminal Velocity

Contributing to the danger of large hailstones is the fact that they fall faster than small ones. That is, the terminal velocity increases with the size of the hailstone. Assuming the hailstones to be spherical and using a drag coefficient of C = 0.5 gives the following :